The texts used range from religious readings (Christian, jewish, Muslim, Hindu, etc), philosophy, quotes by wise people, and poetry. UUs pull inspiration from all of human experience.
RE classes are exactly as you describe - for the preschoolers, we teach more about our core values and being UU (what are the 7 principles, how to be a good friend, how to care for your community, seeing wonder in the natural world, celebrate diversity, etc), but the older classes (1s grade on up) they get into world religions.
Most UU churches have active social justice committees, and working for peace and tolerance are BIG focus areas.
Each church is different - some feel more classically Christian, some more pagan, some more secular humanist (and don't call themselves churches). And within each church, there can be different groups of people who are looking for similar things - at our church, the parents of young kids tend to spend a lot of time together and we are setting up a parents ministry pretty soon because we all need to discuss questions like "how do I explain death to a 4 year old" or "how do I answer questions about God when I am not sure myself?"
Go to the UUA website -
http://www.uua.org/aboutus/findcongregation/index.php to find a congregation near where you will be living.
Good luck and I hope you find UU is a good fit for you! Even if it isn't, I think you'll find the folks very encouraging and welcoming for your spiritual journey.